https://doi.org/10.1140/epjb/e2004-00220-0
Splitting rules for the 2nd hierarchy structure of the electronic spectra of 2D FC(n) quasicrystals
Institute of Laser Life Science, South China Normal
University, Guangzhou 510631, P.R. China
Corresponding author: a xbyang@scnu.edu.cn
Received:
18
March
2004
Published online:
23
July
2004
On the basis of our former work
and by means of the decomposition-decimation method, we study the
splitting rules for the second hierarchy of the electronic energy
spectra for two-dimensional Fibonacci-class quasicrystals with one
kind of atom and two bond lengths. It is found that every line of
the sub-spectra for 
and 
clusters
of FC(n) 
splits according to the type
and type 
respectively. The one for 
clusters of FC(n) consists of three sub-subbands
when 
, and five sub-subbranches when 
. The
general formulae of the number of energy levels for the spectra of
the second hierarchy are obtained. The analytical results are
confirmed by numerical simulations.
PACS: 71.23.Ft – Quasicrystals / 63.90.+t – Other topics in lattice dynamics (restricted to new topics in section 63) / 33.70.Jg – Line and band widths, shapes, and shifts
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2004
